CN113848802B - Dynamic high-speed nested look-ahead planning method - Google Patents

Dynamic high-speed nested look-ahead planning method Download PDF

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CN113848802B
CN113848802B CN202111190982.1A CN202111190982A CN113848802B CN 113848802 B CN113848802 B CN 113848802B CN 202111190982 A CN202111190982 A CN 202111190982A CN 113848802 B CN113848802 B CN 113848802B
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speed
arc
circular arc
radius
ahead
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CN113848802A (en
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李鹏程
李明宇
田威
廖文和
徐翔
魏德岚
康瑞浩
张奇
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Nanjing University of Aeronautics and Astronautics
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00—Programme-control systems
    • G05B19/02—Programme-control systems electric
    • G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
    • G05B19/19—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by positioning or contouring control systems, e.g. to control position from one programmed point to another or to control movement along a programmed continuous path
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00—Program-control systems
    • G05B2219/30—Nc systems
    • G05B2219/35—Nc in input of data, input till input file format
    • G05B2219/35349—Display part, programmed locus and tool path, traject, dynamic locus

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Abstract

The invention discloses a dynamic high-speed nested look-ahead planning method, which comprises the following steps: calculating an initial value of the radius of the transition arc; detecting the existence of a transition arc, and if the transition arc does not exist, primarily adjusting the radius of the current transition arc; adjusting the radius of the transition arc again; detecting whether the adjustment is excessive; judging whether the speed from the previous arc to the next arc is in an acceleration process or a deceleration process; if the acceleration process is the acceleration process, judging whether the acceleration can be in place, if the acceleration can be in place, not adjusting, otherwise, adjusting the radius of the next circular arc; if the speed is in the deceleration process, judging whether the speed can be decelerated in place, if the speed can be decelerated in place, not adjusting, otherwise, adjusting the radius of the previous arc, and adjusting the speed on the previous arc; and correcting the maximum allowable speed of the circular arc, judging whether the current foresight is the last foresight, and performing nested foresight. The invention utilizes a nesting mode and dynamically adjusts the radius of the transition arc at the same time, thereby improving the processing speed, reducing the processing time and improving the efficiency.

Description

Dynamic high-speed nested look-ahead planning method
Technical Field
The invention belongs to the technical field of numerical control, and particularly relates to a dynamic high-speed nested look-ahead planning method.
Background
Most of medium and low-end numerical control machines basically only have the linear and circular interpolation functions, complex parts to be machined are subjected to approximate fitting by Computer Aided Manufacturing (CAM) software by utilizing continuous linear or circular arcs, and each section of track is interpolated to realize the machining of the complex parts. In order to realize high-speed processing, a transition curve needs to be added at the turning point of the line segment, and a proper look-ahead path planning algorithm and a speed planning algorithm are supplemented to obtain high speed.
The existing path planning mainly includes the following steps: one is the circular arc transition, which is also the most common method. And the second is a transition model represented by a quadratic NURBS circular arc model, but the model is more complex in calculation. And thirdly, spline curve transition and global fitting algorithm. Such as: the Ferguson curve, Cardinal curve, 3-time Bezier curve, 3-time B spline and the like, has large calculation amount and is suitable for high-end machine tools.
In the aspect of speed planning, a classical linear acceleration and deceleration method, an exponential acceleration and deceleration method, a trigonometric function acceleration and deceleration method, an S-type acceleration and deceleration method, a clock-type acceleration and deceleration method, a jump-speed constraint acceleration and deceleration method and a cubic polynomial acceleration and deceleration method are available. Compared with linear acceleration and deceleration methods, the acceleration and deceleration methods are better in performance, but have the defects of difficult calculation and influence on the real-time performance of the system, so that the acceleration and deceleration methods are not suitable for medium and low-end machine tools.
In the aspect of a look-ahead algorithm, although a look-ahead method with a fixed number of segments obtains a better result than single-segment linear acceleration and deceleration, because the connection between the line segments is cut off by selecting the fixed number of segments, the information between the line segments cannot be fully utilized, and the look-ahead method cannot adapt to the variable micro-line segment condition.
The self-adaptive look-ahead method solves the difficulties, but when the number of line segments meeting the conditions is too large, the problem of huge data is caused, and the calculation time is long. Therefore, the adaptive look-ahead algorithm usually sets a maximum look-ahead segment number, but when the maximum look-ahead segment number is too large, the look-ahead efficiency is not improved too much, but the complexity is increased, and the real-time performance is reduced.
Aiming at the self-adaptive forward-looking planning method, the maximum forward-looking segment number needs to be set, but the best forward-looking segment number is not clear in literature at present.
Disclosure of Invention
The invention aims to solve the technical problem of providing a dynamic high-speed nested look-ahead planning method aiming at the defects of the prior art, and the dynamic high-speed nested look-ahead planning method is combined with a linear acceleration and deceleration method and an arc transition mode to realize the dynamic high-speed nested look-ahead planning without the maximum look-ahead segment number and is suitable for a numerical control system for small segment processing.
In order to achieve the technical purpose, the technical scheme adopted by the invention is as follows:
a dynamic high-speed nested look-ahead planning method is characterized by comprising the following steps:
step 1: initializing a transition arc according to the maximum contour error and the maximum bow height error according to each prospective model diagram to obtain an initial value of the radius of the transition arc;
step 2: detecting the existence of a transition circular arc, if not, performing primary adjustment on the radius of the current transition circular arc by using improved midpoint constraint;
and step 3: comparing the speed of the tail section accelerated from the end point to the joint of the next circular arc with the maximum speed allowed by the circular arc, and adjusting the radius of the transition circular arc when the speed is adjusted for the first time when the speed is smaller than the maximum speed or the angle is smaller than 126.8699 degrees;
and 4, step 4: after the adjustment in the step 3 is completed, detecting whether the adjustment in the step 3 is excessive before the next speed constraint is carried out, and if the adjustment is excessive, carrying out the constraint again by using the method in the step 2;
step 5, calculating and comparing the maximum allowable speeds of the two connected arcs, and judging whether the speed from the previous arc to the next arc is an acceleration process or a deceleration process;
if the speed is in the acceleration process, judging whether the speed can be accelerated to the right position by combining with speed planning, namely whether the speed can be accelerated to the maximum allowable speed of the next circular arc, if so, not adjusting, otherwise, adjusting the radius of the next circular arc;
if the speed is in the process of speed reduction, judging whether the speed can be reduced to the maximum allowable speed of the next circular arc or not by combining with speed planning, if so, not adjusting, otherwise, adjusting the radius of the previous circular arc, and then adjusting the speed on the previous circular arc;
step 6: correcting the maximum allowable speed of the arc according to the maximum arch height error, and judging whether the current foresight is the last foresight;
and if the last look ahead is carried out, all data are stored, otherwise, the data of the first straight line and the previous circular arc are stored and stored in a memory, the interpolation of an interpolator is waited, then the next straight line is read, and then the step 1 is returned to carry out the next look ahead, so that the nested look ahead is realized.
In order to optimize the technical scheme, the specific measures adopted further comprise:
in the above step 1, P is shownm-1、Pm、Pn、PqAdopting a strategy of inserting a circular arc segment for the end point of the adjacent line segment, wherein the central point is Om、OnRadius Rm、RnIn which O ism1、Om2、On1、On2Is the tangent point of the arc and the adjacent straight line segment, the segment PmOmIntersects with the circular arc at P1Dot and crossm1Om2In P5Line segment P3P4Perpendicular to PmOmCross-linking of PmOmIn P2Line segment P1P2Length of (2)
Figure GDA0003504931890000021
Indicates the bow height error e generated by the maximum interpolation speed allowed by the transition circular arcchLine segment P2PmLength of (2)
Figure GDA0003504931890000022
Indicating the profile error e generated by the maximum interpolation speed allowed by the transition arcco；
The radius of the arc is then:
rm＝sin(θ/2)×(eco-ech)/(1-sin(θ/2))
the current planning transition segment is Pm-1PmPnPqSegment, maximum profile error allowed by the system is eco_maxThe maximum allowable bow height error of the system is ech_maxStraight line segment Pm-1PmPnIs theta1Straight line segment PmPnPqIs theta2；
The length of each segment of the transition arc is:
r1＝sin(θ1/2)×(eco_max-ech_max)/(1-sin(θ1/2))
Figure GDA0003504931890000031
r2＝sin(θ2/2)×(eco_max-ech_max)/(1-sin(θ2/2))
Figure GDA0003504931890000032
Figure GDA0003504931890000033
the initial value of the transition arc radius is:
r＝sin(θ/2)×(eco_max-ech_max)/(1-sin(θ/2))
wherein e isco_maxMaximum profile error allowed for the system, ech_maxTheta is the angle between the segments, which is the maximum bow height error allowed by the system.
In the above step 2, when
Figure GDA0003504931890000034
If so, indicating that the arc does not exist, and needing to perform primary adjustment on the radius of the arc;
when in use
Figure GDA0003504931890000035
If at least one arc does not exist, the arc needs to be preliminarily adjusted, the tangent point of the arc and the straight line is adjusted to the middle point of the straight line, and the parameters are updated;
when in use
Figure GDA0003504931890000036
The initial adjustment is carried out by adopting an improved midpoint constraint method:
when in use
Figure GDA0003504931890000037
When, if
Figure GDA0003504931890000038
If larger, the adjustment is:
Figure GDA0003504931890000039
will be provided with
Figure GDA00035049318900000310
If larger, the adjustment is:
Figure GDA00035049318900000311
when in use
Figure GDA00035049318900000312
Then, all are adjusted to half of the length of the straight line, i.e.
Figure GDA00035049318900000313
And updates the parameters.
In the step 3, if the transition arc is adjusted for the first time when the angle is smaller than 126.8699 °, the radius of the transition arc is adjusted, specifically:
according to the condition needing to be adjusted, if the condition is met, the speed of accelerating from 0 to the starting point of the next circular arc is equal to the speed on the next circular arc according to the prospective terminal point and speed plan, the length of the deceleration stage is worked out, the radius of the next transition circular arc is worked out according to a relational expression, and the radius of the transition circular arc is adjusted;
the same applies to the first arc if the first look ahead is taken.
In step 5, the maximum allowable speed of the previous arc is:
the minimum of the velocities allowed by the kinetics on the arc and the velocity projected from the starting point binding velocity to the ligation point;
the maximum allowable speed for the latter arc is:
the minimum of the two velocities allowed by the dynamics on the arc and the velocity accelerated from the end point back from 0 to the arc's joining point.
In the step 5, the determining whether the speed from the previous arc to the next arc is an acceleration process or a deceleration process specifically includes:
if the maximum allowable speed of the previous circular arc is less than that of the next circular arc, the process is accelerated; otherwise, it is a deceleration process.
In the step 5, the determining whether the acceleration can be performed in place in combination with the speed plan specifically includes:
the exit speed of the previous arc is combined with the speed planning, if the speed of the joining point of the next arc is higher than that of the next arc, the joining point can be accelerated to the right position, otherwise, the joining point cannot be accelerated to the right position;
the speed planning is used for judging whether the speed can be reduced to the maximum allowable speed of the next circular arc or not, and the specific steps are as follows:
and combining the exit speed of the latter arc with speed planning, if the speed of the joining point of the former arc is higher than that of the former arc, decelerating to the maximum allowable speed of the next arc, otherwise, not decelerating to the maximum allowable speed of the next arc.
In the step 5, the adjusting the radius of the last circular arc specifically includes:
the speed of the front arc end point combined with the speed plan to accelerate to the starting point of the back arc is equal to the speed on the back arc, the length of the acceleration stage is calculated, and then the radius of the back arc is calculated by combining a relational expression;
the adjusting of the radius of the previous arc specifically comprises:
the speed of the backward acceleration to the end point of the previous circular arc is equal to the speed on the previous circular arc by combining the speed planning from the starting point of the next circular arc, the length of the deceleration stage is worked out, and the radius of the previous circular arc is worked out by combining a relational expression;
the adjusting of the speed of the previous arc specifically comprises:
calculating the point On1Is accelerated reversely to the point Om2Velocity of point PnIs accelerated from the speed of 0 to the point Om2The minimum value of the speed and the limited maximum speed is set as the maximum allowable speed of the circular arc.
In the step 6, the correcting the maximum allowable speed of the arc according to the maximum bow height error specifically includes:
after acceleration and deceleration constraints, the allowable speed of the previous circular arc under the constraint of the maximum bow height error is calculated, and the minimum value of the two is taken.
In the above step 6, after the current look-ahead is finished, only the data of the first straight line and the first arc are stored, and the remaining line segments, the remaining arcs, and the new line segment are introduced to the next look-ahead, so that the nested look-ahead is realized.
The invention has the following beneficial effects:
1. the invention provides a method for dynamically adjusting a transition arc, which reduces the radius of the arc and improves the contour precision during processing.
2. The invention provides a method based on nested look-ahead, which does not need to specify the maximum look-ahead segment number and realizes multi-segment planning in a nested mode.
3. The invention utilizes the modes of nested look-ahead and dynamic adjustment of the radius of the transition arc, improves the maximum speed in the path planning process, improves the processing efficiency, and can predict the deceleration point in advance and decelerate in advance.
Drawings
FIG. 1 is a schematic view of a circular arc transition model;
FIG. 2 is a flow chart of the method of the present invention;
FIG. 3 illustrates a manner of initial adjustment of the transition arc;
FIG. 4 is a diagram of an original path;
FIG. 5 is a transition arc planned for a conventional machining method;
FIG. 6 is a velocity profile planned for a conventional machining method;
FIG. 7 is a transition arc contemplated by the present invention;
FIG. 8 is a velocity profile of the process of the present invention.
Detailed Description
Embodiments of the present invention are described in further detail below with reference to the accompanying drawings.
Referring to fig. 2, a dynamic high-speed nested look-ahead planning method includes:
step 1: initializing transition arcs according to the maximum contour error and the maximum arch height error according to each look-ahead model diagram shown in FIG. 1, wherein the initialized radius of the previous arc is the radius of the next transition arc in the last look-ahead, and obtaining the initial value of the radius of the transition arcs;
in the examples, P ism-1、Pm、Pn、PqFor the end points of adjacent line segments and for realizing smooth transition between the adjacent line segments, a strategy of inserting a circular arc segment is adopted, and the central point is Om、OnRadius Rm、RnIn which O ism1、Om2、On1、On2Is the tangent point of the arc and the adjacent straight line segment, the segment PmOmIntersects with the circular arc at P1Dot and crossm1Om2In P5Line segment P3P4Perpendicular to PmOmCross-linking of PmOmIn P2Line segment P1P2Length of (2)
Figure GDA0003504931890000061
Indicates the bow height error e generated by the maximum interpolation speed allowed by the transition circular arcchLine segment P2PmLength of (2)
Figure GDA0003504931890000062
Indicating the profile error e generated by the maximum interpolation speed allowed by the transition arcco；
The radius of the arc is then:
rm＝sin(θ/2)×(eco-ech)/(1-sin(θ/2))
the current planning transition segment is Pm-1PmPnPqSegment, maximum profile error allowed by the system is eco_maxThe maximum allowable bow height error of the system is ech_maxStraight line segment Pm-1PmPnIs theta1Straight line segment PmPnPqIs theta2；
The length of each segment of the transition arc is:
r1＝sin(θ1/2)×(eco_max-ech_max)/(1-sin(θ1/2))
Figure GDA0003504931890000063
r2＝sin(θ2/2)×(eco_max-ech_max)/(1-sin(θ2/2))
Figure GDA0003504931890000064
Figure GDA0003504931890000065
the initial value of the transition arc radius is:
r＝sin(θ/2)×(eco_max-ech_max)/(1-sin(θ/2))
wherein e isco_maxMaximum profile error allowed for the system, ech_maxTheta is the angle between the segments, which is the maximum bow height error allowed by the system.
Step 2: detecting the existence of a transition circular arc, if not, performing primary adjustment on the radius of the current transition circular arc by using improved midpoint constraint;
when in use
Figure GDA0003504931890000066
If so, indicating that the arc does not exist, and needing to perform primary adjustment on the radius of the arc;
when in use
Figure GDA0003504931890000067
If at least one circular arc does not exist, the initial adjustment is needed to make the tangent point O of the circular arc and the straight linem1(or O)n2) Adjusted to a straight line Pm-1Pm(or P)nPq) And updating the parameters;
when in use
Figure GDA0003504931890000071
Here, an improved midpoint constraint method is used for initial adjustment.
When in use
Figure GDA0003504931890000072
When, if
Figure GDA0003504931890000073
If larger, the adjustment is:
Figure GDA0003504931890000074
will be provided with
Figure GDA0003504931890000075
If larger, the adjustment is:
Figure GDA0003504931890000076
as shown in FIG. 3(a) below;
when in use
Figure GDA0003504931890000077
Then, all are adjusted to half of the length of the straight line, i.e.
Figure GDA0003504931890000078
As shown in fig. 3(b) below. And updates the parameters.
And step 3: and (3) adjusting the radius of the transition arc again:
comparing the speed of the tail segment accelerated from the end point to the joint of the next circular arc with the maximum allowable speed of the circular arc, and if the speed is smaller than the maximum allowable speed, or the angle is smaller than 126.8699 degrees, the radius of the transition circular arc is adjusted for the first time:
according to the condition needing to be adjusted, if the condition is met, the speed of accelerating from 0 to the starting point of the next circular arc is equal to the speed on the next circular arc according to the prospective terminal point combined speed plan, the length of the deceleration stage can be obtained, the radius of the next transition circular arc can be obtained by combining a relational expression, and then the radius of the circular arc is adjusted. If the first look ahead is obtained, the same applies to the first arc.
And 4, step 4: after the adjustment in the step 3 is completed, detecting whether the adjustment in the step 3 is excessive before the next speed constraint is carried out, and if the adjustment is excessive, carrying out the constraint again by using the method in the step 2;
that is, after adjustment, the radius of the arc originally meeting the condition is adjusted to be larger, so that the arc does not exist, and therefore, after adjustment, detection and adjustment are required to be performed again according to the step of primary adjustment of the transition arc, and the adjustment at this time is as described in step 2.
Step 5, calculating and comparing the maximum allowable speeds of the two connected arcs (the maximum allowable speed of the previous arc is the minimum value of the speed allowed by the dynamics on the arc and the speed planned to the connection point from the starting point to the speed combined with the speed, and the maximum allowable speed of the next arc is the minimum value of the speed allowed by the dynamics on the arc and the speed reversely accelerated from the terminal point to the connection point of the arcs), and judging whether the speed from the previous arc to the next arc is an acceleration process or a deceleration process (if the maximum allowable speed of the previous arc is less than the maximum allowable speed of the next arc, the acceleration process is carried out, otherwise, the deceleration process is carried out);
if the speed is the acceleration process, whether the acceleration can be in place or not is judged by combining the speed plan (the exit speed of the previous circular arc is combined with the speed plan, if the speed to the joint point of the previous circular arc is greater than the speed of the next circular arc, the acceleration can be in place, otherwise, the acceleration cannot be in place), namely, whether the acceleration can be in place or not is judged, if the speed to the joint point of the previous circular arc is greater than the speed of the next circular arc, the adjustment is not carried out, otherwise, the radius of the next circular arc is adjusted (the speed accelerated to the starting point of the next circular arc by combining the speed plan of the end point of the previous circular arc is equal to the speed on the next circular arc, the length of the acceleration stage is calculated, and then the radius of the next circular arc is calculated by combining the relational expression).
If the speed is the deceleration process, the speed plan is combined to judge whether the speed can be decelerated to the maximum allowable speed of the next circular arc (the exit speed of the next circular arc is combined with the speed plan, if the speed to the joint point of the previous circular arc is greater than the speed of the previous circular arc, the speed can be decelerated to the maximum allowable speed of the next circular arc, otherwise, the speed cannot be decelerated to the maximum allowable speed of the next circular arcDegree), if possible, then not adjusting, otherwise adjusting the radius of the previous arc (the speed of the backward acceleration from the starting point of the next arc to the end point of the previous arc in combination with the speed plan is equal to the speed on the previous arc, calculating the length of the deceleration stage, combining the relational expression to calculate the radius of the previous arc), then adjusting the speed on the previous arc (the calculation point On1Is accelerated reversely to the point Om2Velocity of point PnIs accelerated from the speed of 0 to the point Om2The minimum value of the speed at (b) and the defined maximum speed is set as the maximum allowable speed of the arc).
The step 5 specifically comprises the following steps:
setting the maximum allowable speed v on the previous circular arcmcCorresponding to an angle of thetamMaximum allowable velocity v on the latter arcncCorresponding to an angle of thetan。
If v ismc＞vncIn the line segment PmPnThe whole body is in a deceleration state, and the straight line O ism2On1Outlet velocity vn1
Figure GDA0003504931890000081
vn1＜vncWhen it is, the transition arc does not need to be adjusted, if vn1＞vncThen the speed of the previous transition arc needs to be adjusted. At this time, forward adjustment is needed, and the adjustment method is as follows: the speed of the backward acceleration to the end point of the previous circular arc is equal to the speed on the previous circular arc by combining the speed planning from the starting point of the next circular arc, so that the length of the deceleration stage can be obtained, and the radius of the previous circular arc can be obtained by combining a relational expression. Updating the circular arc velocity vmcAnd calculates the point PnReverse acceleration from 0 to point Om2Velocity v ofOm2', and by point On1Acceleration to O in conjunction with velocity planningm2Velocity of a point
Figure GDA0003504931890000082
Second, at θm＞126.8699°，
Figure GDA0003504931890000083
At thetam＜126.8699°，
Figure GDA0003504931890000084
To ensure that the next arc is smoothly joined, point O is setm2The velocity at the point should satisfy:
Figure GDA0003504931890000085
if v ismc≤vncIn the line segment PmPnThe whole body is in an acceleration state, at the time of a straight line Om2On1Upper outlet velocity
Figure GDA0003504931890000086
Satisfy vn1＞vncIf so, the radius of the transition arc is not adjusted, and if v isn1＜vncWhile, then the transition arc O is reducednThe radius of (2) can increase the length of the acceleration stage and can also reduce the magnitude of the terminal velocity. The speed of the last circular arc from the end point of the previous circular arc combined with the speed plan to the starting point of the next circular arc is equal to the speed on the next circular arc, the acceleration length can be obtained, and then the radius of the next circular arc can be obtained by combining the relational expression. And updates the velocity vnc、vn1With position parameter, velocity adjusted to vnc＝vn1＝min{vnc,vn1}；
Step 6: correcting the maximum allowable speed of the arc according to the maximum arch height error, and judging whether the current foresight is the last foresight;
and if the last look-ahead is carried out, all data are stored, otherwise, the data of the first straight line and the previous circular arc are stored in the memory, the interpolation of the interpolator is waited, then the next straight line is read, and then the step 1 is returned to carry out the next look-ahead, so that the nested look-ahead is realized (namely, a new line segment is introduced to carry out the nested look-ahead processing).
The maximum allowable speed of the arc is corrected according to the maximum height error of the arc, and the method specifically comprises the following steps:
the maximum allowable feed speed of the transition arc under the maximum bow height error is as follows:
Figure GDA0003504931890000091
in the formula, TsFor the interpolation period, R is the radius of the arc.
Then the arc of a circle OmThe speed adjustment of (1) is:
vmc＝vm0＝min{v,vmc}
if the current look ahead is the last look ahead, all data are stored, if the current look ahead is not the last look ahead, the data of a first straight line and a previous circular arc are stored, interpolation of an interpolator is waited, then the next straight line is read, and then the next look ahead is carried out. And then the content of the steps 1-6 is circulated.
The effects of the embodiment are as follows:
the maximum allowable speed of the Cartesian space is set to be 300mm/s, and the maximum acceleration is set to be 1000mm/s2The maximum profile error is 0.05mm, the maximum bow height error is 0.01mm, the interpolation period is 1ms, the path to be planned is shown in fig. 4, and the point location data of the path to be planned is shown in table 1. Fig. 5-6 show results of processing using conventional methods, and fig. 7-8 show results of processing using the methods herein. The radius of the transition arc is reduced in the machining process, and the profile error is smaller. The velocity profile during the processing is shown in fig. 6 and 8, the traditional method takes 1116ms, the method takes 576ms, and the highest velocity obtained by the method is higher than that obtained by the traditional method. Overall time consumption is shorter, speed is higher, and contour accuracy is better.
TABLE 1 Point location data of the path to be planned
Figure GDA0003504931890000092
Figure GDA0003504931890000101
By means of the nesting mode, the maximum forward-looking segment number does not need to be specified, and meanwhile, a method for dynamically planning the transition arc is integrated, so that the processing speed is increased, and the processing time is shortened. The radius of the arc becomes smaller, and the machining accuracy is also improved appropriately.
The above is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above-mentioned embodiments, and all technical solutions belonging to the idea of the present invention belong to the protection scope of the present invention. It should be noted that modifications and embellishments within the scope of the invention may be made by those skilled in the art without departing from the principle of the invention.

Claims (10)

1. A dynamic high-speed nested look-ahead planning method is characterized by comprising the following steps:
step 1: initializing a transition arc according to the maximum contour error and the maximum bow height error according to each prospective model diagram to obtain an initial value of the radius of the transition arc;
step 2: detecting the existence of a transition circular arc, if not, performing primary adjustment on the radius of the current transition circular arc by using improved midpoint constraint;
and step 3: comparing the speed of the tail section accelerated from the end point to the joint of the next circular arc with the maximum speed allowed by the circular arc, and adjusting the radius of the transition circular arc when the speed is adjusted for the first time when the speed is smaller than the maximum speed or the angle is smaller than 126.8699 degrees;
and 4, step 4: after the adjustment in the step 3 is completed, detecting whether the adjustment in the step 3 is excessive before the next speed constraint is carried out, and if the adjustment is excessive, carrying out the constraint again by using the method in the step 2;
step 5, calculating and comparing the maximum allowable speeds of the two connected arcs, and judging whether the speed from the previous arc to the next arc is an acceleration process or a deceleration process;
if the speed is in the acceleration process, judging whether the speed can be accelerated to the right position by combining with speed planning, namely whether the speed can be accelerated to the maximum allowable speed of the next circular arc, if so, not adjusting, otherwise, adjusting the radius of the next circular arc;
if the speed is in the process of speed reduction, judging whether the speed can be reduced to the maximum allowable speed of the next circular arc or not by combining with speed planning, if so, not adjusting, otherwise, adjusting the radius of the previous circular arc, and then adjusting the speed on the previous circular arc;
step 6: correcting the maximum allowable speed of the arc according to the maximum arch height error, and judging whether the current foresight is the last foresight;
and if the last look ahead is carried out, all data are stored, otherwise, the data of the first straight line and the previous circular arc are stored and stored in a memory, the interpolation of an interpolator is waited, then the next straight line is read, and then the step 1 is returned to carry out the next look ahead, so that the nested look ahead is realized.
2. The dynamic high-speed nested look-ahead planning method of claim 1, wherein in step 1, P is writtenm-1、Pm、Pn、PqAdopting a strategy of inserting a circular arc segment for the end point of the adjacent line segment, wherein the central point is Om、OnRadius Rm、RnIn which O ism1、Om2、On1、On2Is the tangent point of the arc and the adjacent straight line segment, the segment PmOmIntersects with the circular arc at P1Dot and crossm1Om2In P5Line segment P3P4Perpendicular to PmOmCross-linking of PmOmIn P2Line segment P1P2Length of (2)
Figure FDA0003504931880000011
Indicates the bow height error e generated by the maximum interpolation speed allowed by the transition circular arcchLine segment P2PmLength of (2)
Figure FDA0003504931880000012
Indicating the profile error e generated by the maximum interpolation speed allowed by the transition arcco；
The radius of the arc is then:
rm＝sin(θ/2)×(eco-ech)/(1-sin(θ/2))
the current planning transition segment is Pm-1PmPnPqSegment, maximum profile error allowed by the system is eco_maxThe maximum allowable bow height error of the system is ech_maxStraight line segment Pm-1PmPnIs theta1Straight line segment PmPnPqIs theta2；
The length of each segment of the transition arc is:
r1＝sin(θ1/2)×(eco_max-ech_max)/(1-sin(θ1/2))
Figure FDA0003504931880000021
r2＝sin(θ2/2)×(eco_max-ech_max)/(1-sin(θ2/2))
Figure FDA0003504931880000022
Figure FDA0003504931880000023
the initial value of the transition arc radius is:
r＝sin(θ/2)×(eco_max-ech_max)/(1-sin(θ/2))
wherein e isco_maxMaximum profile error allowed for the system, ech_maxTheta is the angle between the segments, which is the maximum bow height error allowed by the system.
3. The method as claimed in claim 2, wherein the step 2 is a step of performing a nested look-ahead planningWhen is coming into contact with
Figure FDA0003504931880000024
If so, indicating that the arc does not exist, and needing to perform primary adjustment on the radius of the arc;
when in use
Figure FDA0003504931880000025
If at least one arc does not exist, the arc needs to be preliminarily adjusted, the tangent point of the arc and the straight line is adjusted to the middle point of the straight line, and the parameters are updated;
when in use
Figure FDA0003504931880000026
The initial adjustment is carried out by adopting an improved midpoint constraint method:
when in use
Figure FDA0003504931880000027
When, if
Figure FDA0003504931880000028
If larger, the adjustment is:
Figure FDA0003504931880000029
will be provided with
Figure FDA00035049318800000210
If larger, the adjustment is:
Figure FDA00035049318800000211
when in use
Figure FDA00035049318800000212
Then, all are adjusted to half of the length of the straight line, i.e.
Figure FDA00035049318800000213
And updates the parameters.
4. A dynamic high-speed nested look-ahead planning method according to any one of claims 1 to 3, wherein in step 3, if the transition arc is adjusted for the first time in the case of being smaller than the predetermined value or when the angle is smaller than 126.8699 °, the radius of the transition arc is adjusted, specifically:
according to the condition needing to be adjusted, if the condition is met, the speed of accelerating from 0 to the starting point of the next circular arc is equal to the speed on the next circular arc according to the prospective terminal point and speed plan, the length of the deceleration stage is worked out, the radius of the next transition circular arc is worked out according to a relational expression, and the radius of the transition circular arc is adjusted;
the same applies to the first arc if the first look ahead is taken.
5. A dynamic high-speed nested look-ahead planning method according to any one of claims 1-3, in which in step 5, the maximum allowable speed of the previous arc is:
the minimum of the velocities allowed by the kinetics on the arc and the velocity projected from the starting point binding velocity to the ligation point;
the maximum allowable speed for the latter arc is:
the minimum of the two velocities allowed by the dynamics on the arc and the velocity accelerated from the end point back from 0 to the arc's joining point.
6. The dynamic high-speed nested look-ahead planning method according to any one of claims 1 to 3, wherein in step 5, the determining whether the speed from the previous arc to the next arc is in an acceleration process or a deceleration process is specifically:
if the maximum allowable speed of the previous circular arc is less than that of the next circular arc, the process is accelerated; otherwise, it is a deceleration process.
7. The dynamic high-speed nested look-ahead planning method according to any one of claims 1 to 3, wherein in step 5, the determining whether acceleration can be achieved in place in combination with speed planning specifically includes:
the exit speed of the previous arc is combined with the speed planning, if the speed of the joining point of the next arc is higher than that of the next arc, the joining point can be accelerated to the right position, otherwise, the joining point cannot be accelerated to the right position;
the speed planning is used for judging whether the speed can be reduced to the maximum allowable speed of the next circular arc or not, and the specific steps are as follows:
and combining the exit speed of the latter arc with speed planning, if the speed of the joining point of the former arc is higher than that of the former arc, decelerating to the maximum allowable speed of the next arc, otherwise, not decelerating to the maximum allowable speed of the next arc.
8. The dynamic high-speed nested look-ahead planning method according to claim 2 or 3, wherein in step 5, the adjusting of the radius of the next circular arc specifically includes:
the speed of the front arc end point combined with the speed plan to accelerate to the starting point of the back arc is equal to the speed on the back arc, the length of the acceleration stage is calculated, and then the radius of the back arc is calculated by combining a relational expression;
the adjusting of the radius of the previous arc specifically comprises:
the speed of the backward acceleration to the end point of the previous circular arc is equal to the speed on the previous circular arc by combining the speed planning from the starting point of the next circular arc, the length of the deceleration stage is worked out, and the radius of the previous circular arc is worked out by combining a relational expression;
the adjusting of the speed of the previous arc specifically comprises:
calculating the point On1Is accelerated reversely to the point Om2Velocity of point PnIs accelerated from the speed of 0 to the point Om2The minimum value of the speed and the limited maximum speed is set as the maximum allowable speed of the circular arc.
9. The dynamic high-speed nested look-ahead planning method according to claim 1, wherein in step 6, the maximum allowable speed of the arc is corrected according to the maximum bow height error, specifically:
after acceleration and deceleration constraints, the allowable speed of the previous circular arc under the constraint of the maximum bow height error is calculated, and the minimum value of the two is taken.
10. The dynamic high-speed nested look-ahead planning method of claim 1, wherein in step 6, after the current look-ahead is finished, only the data of the first straight line and the first circular arc are saved, and the rest line segments and circular arcs and the line segment of the new line are introduced to the next look-ahead, so as to realize the nested look-ahead.
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